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PreprintCC BY 4.0arXiv

Cohomological beta function

  • Oleksandr Gamayun
  • Maxim Gritskov
  • Andrey Losev
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Abstract

We propose a cohomological approach to computing the conformal anomaly. Using the example of current-current deformations of two-dimensional conformal field theories, we reproduce the well-known Cardy formula for the leading contribution to the perturbative beta function as the coefficient of the cocycle that realizes the obstruction to deforming the conformal algebra module structure on the state space. In addition to offering a novel conceptual perspective on the conformal anomaly, the proposed approach is anticipated to provide an efficient tool for computing higher-order coefficients of perturbative beta functions.

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Cite

BibTeXRIS
BibTeX
@misc{gamayun2026cohomological,
  title = {{Cohomological beta function}},
  author = {Oleksandr Gamayun and Maxim Gritskov and Andrey Losev},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.28975},
  eprint = {2606.28975},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.28975},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Cohomological beta function
AU  - Oleksandr Gamayun
AU  - Maxim Gritskov
AU  - Andrey Losev
PY  - 2026
DA  - 2026/10/16
PB  - arXiv
DO  - 10.48550/arxiv.2606.28975
UR  - https://arxiv.org/abs/2606.28975
AB  - We propose a cohomological approach to computing the conformal anomaly. Using the example of current-current deformations of two-dimensional conformal field theories, we reproduce the well-known Cardy formula for the leading contribution to the perturbative beta function as the coefficient of the cocycle that realizes the obstruction to deforming the conformal algebra module structure on the state space. In addition to offering a novel conceptual perspective on the conformal anomaly, the proposed approach is anticipated to provide an efficient tool for computing higher-order coefficients of perturbative beta functions.
ER  -